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Spectrum and entropy of C-systems MIXMAX random number generator

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  • Savvidy, Konstantin
  • Savvidy, George

Abstract

The uniformly hyperbolic Anosov C-systems defined on a torus have very strong instability of their trajectories, as strong as it can be in principle. These systems have exponential instability of all their trajectories and as such have mixing of all orders, nonzero Kolmogorov entropy and a countable set of everywhere dense periodic trajectories. In this paper we are studying the properties of their spectrum and of the entropy. For a two-parameter family of C-system operators A(N, s), parameterised by the integers N and s, we found the universal limiting form of the spectrum, the dependence of entropy on N and the period of its trajectories on a rational sublattice. One can deduce from this result that the entropy and the periods are sharply increasing with N. We present a new three-parameter family of C-operators A(N, s, m) and analyse the dependence of its spectrum and of the entropy on the parameter m. We are developing our earlier suggestion to use these tuneable Anosov C-systems for multipurpose Monte-Carlo simulations. The MIXMAX family of random number generators based on Anosov C-systems provide high quality statistical properties, thanks to their large entropy, have the best combination of speed, reasonable size of the state, tuneable parameters and availability for implementing the parallelisation.

Suggested Citation

  • Savvidy, Konstantin & Savvidy, George, 2016. "Spectrum and entropy of C-systems MIXMAX random number generator," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 33-38.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:33-38
    DOI: 10.1016/j.chaos.2016.05.003
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    References listed on IDEAS

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    1. G. G. Athanasiu & E. G. Floratos & G. K. Savvidy, 1997. "K-System Generator of Pseudorandom Numbers on Galois Field," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 555-565.
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    Cited by:

    1. Savvidy, George & Savvidy, Konstantin, 2018. "Exponential decay of correlations functions in MIXMAX generator of pseudorandom numbers," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 244-250.
    2. Martirosyan, Narek & Savvidy, Konstantin & Savvidy, George, 2019. "Spectral test of the MIXMAX random number generators," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 242-248.
    3. Pierre L’Ecuyer & Paul Wambergue & Erwan Bourceret, 2020. "Spectral Analysis of the MIXMAX Random Number Generators," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 135-144, January.

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